Existence and regularizing rate estimates of mild solutions to a generalized magneto-hydrodynamic system in Q-spaces

摘要

We study existence of mild solution to a n-dimensional generalized incompressible magneto-hydrodynamic (GMHD) system with initial value （uo,bo) in a new critical space (Q_(α,∞)~(β,-1)(R~n))~(2n)：= (▽. (Q_α~β(R~n))~n)~(2n)， and Q_α~β(R~n) is the space of all measurable functions f on Rn satisfying where the supremum is taken over all cubes I with the edge length l(I) and the edges parallel to the coordinate axes in R~n. The regularizing rate estimates for the 7th spatial derivatives of solution are also proved, which imply the spatial analyticity of the solution and temporal decay of global solution.